Big Idea: Negative numbers help us to model many real world situations. Essential Question: How do I multiply and divide integers. Problem 4.2
A. Describe any patterns you observe in the way the products change as the integers multiplied by 5 get smaller.
The products are decreasing by 5, as the multiplier is decreasing by 1.
B. 1. Use the patterns you observed to predict 5 x -1. Explain your reasoning.
Since the product decreases by 5 each time, and -1 is just one unit below 0, I will subtract 5 from the previous product. The previous product was 0 so 0 – 5= -5. The answer is -5.
C. Complete the equations below, and use them to help you answer parts D and E.
5 x -4= -20
4 x -4= -16
3 x -4= -12
2 x -4= -8
1 x -4= -4
0 x -4= 0
D. Describe any patterns you observe in the way the products change, as the integers multiplied by -4 get smaller.
The products of the equations are increasing by 4 as the number being multiplied with -4 get smaller.
E. 1.Use the patterns you observed to predict -1 x -4. Explain your reasoning.
Since the product increases by 4 each time, and -1 is just one unit below 0, I will add 4 to the previous product. The previous product was 0 so 0 + 4= 4. The answer is +4
2. Write the next four equations in the pattern.
-2 x -4= 8
-3 x -4= 12
-4 x -4= 16
-5 x -4= 20
-6 x -4= 24
-7 x -4= 28
F. Find the following products.
1. -3 x 7= -21
2. 5 x -8= -40
3. -11 x -12= 132
4. -3.6 x 2.7= -9.72
Problem 4.2 Follow-Up
1. a. Find -6 x 7 and 7 x -6.
-6 x 7= -42 and 7 x -6= -42
b. When you multiply integers, does the order of the numbers matter?
No, because whatever the order is, the product will always be the same.
2. a. Find -6 + 7 and 7 + -6.
-6 + 7= 1 and 7 + -6= 1
b. When you add integers, does the order of the numbers matter?
No, because whatever the order is, the sum will always be the same.
3. a. Find -6 – 7 and 7 - -6. -6 – 7= -13 and 7 - -6= 13
b. When you subtract integers, does the order of the numbers matter?
Yes, the order does matter because switching the order will give you the opposite of the normal difference.
4. When you add two negative integers, you get a negative result. Is the same true when you multiply two negative integers? Explain.
The same is not true because multiplying a negative integer with a negative integer will give a product that is positive.
April 27, 10
Math 7B
Big Idea: Negative numbers help us to model many real world situations.
Essential Question: How do I multiply and divide integers.
Problem 4.2
A. Describe any patterns you observe in the way the products change as the integers multiplied by 5 get smaller.
The products are decreasing by 5, as the multiplier is decreasing by 1.
B. 1. Use the patterns you observed to predict 5 x -1. Explain your reasoning.
Since the product decreases by 5 each time, and -1 is just one unit below 0, I will subtract 5 from the previous product. The previous product was 0 so 0 – 5= -5. The answer is -5.
C. Complete the equations below, and use them to help you answer parts D and E.
5 x -4= -20
4 x -4= -16
3 x -4= -12
2 x -4= -8
1 x -4= -4
0 x -4= 0
D. Describe any patterns you observe in the way the products change, as the integers multiplied by -4 get smaller.
The products of the equations are increasing by 4 as the number being multiplied with -4 get smaller.
E. 1. Use the patterns you observed to predict -1 x -4. Explain your reasoning.
Since the product increases by 4 each time, and -1 is just one unit below 0, I will add 4 to the previous product. The previous product was 0 so 0 + 4= 4. The answer is +4
2. Write the next four equations in the pattern.
-2 x -4= 8
-3 x -4= 12
-4 x -4= 16
-5 x -4= 20
-6 x -4= 24
-7 x -4= 28
F. Find the following products.
1. -3 x 7= -21
2. 5 x -8= -40
3. -11 x -12= 132
4. -3.6 x 2.7= -9.72
1. a. Find -6 x 7 and 7 x -6.
-6 x 7= -42 and 7 x -6= -42
b. When you multiply integers, does the order of the numbers matter?
No, because whatever the order is, the product will always be the same.
2. a. Find -6 + 7 and 7 + -6.
-6 + 7= 1 and 7 + -6= 1
b. When you add integers, does the order of the numbers matter?
No, because whatever the order is, the sum will always be the same.
3. a. Find -6 – 7 and 7 - -6.
-6 – 7= -13 and 7 - -6= 13
b. When you subtract integers, does the order of the numbers matter?
Yes, the order does matter because switching the order will give you the opposite of the normal difference.
4. When you add two negative integers, you get a negative result. Is the same true when you multiply two negative integers? Explain.
The same is not true because multiplying a negative integer with a negative integer will give a product that is positive.